Question

solve
4cos^2 2a-4 sinA-1=0

Answer 1

4cos​2A - 4sinA - 1 = 0
4(1-sin​2A) - 4sinA - 1 = 0
4 - 4sin​2A - 4sinA - 1 = 0
- 4sin2A - 4sinA + 3 = 0
4sin2A + 4sinA - 3 = 0
4sin2A - 2sinA + 6sinA - 3 = 0
2sinA(2sinA - 1) + 3(2sinA - 1) = 0
(2sinA - 1) (2sinA + 3) = 0
2sinA - 1 = 0 OR 2sinA + 3 = 0
sinA = 1/2 OR sinA = -3/2
Since range of sine is [-1,1]
Therefore, sinA = -3/2 is not possible
Thus, only answer is sinA = 1/2
A = 60° or 120°